Automated detection of proliferative retinopathy in clinical practice

ImageJ in Computational Fractal-Based Neuroscience: Pattern Extraction and Translational Research

To explore questions asked in neuroscience, neuroscientists rely heavily on the tools available. One such toolset is ImageJ, open-source, free, biological digital image analysis software. Open-source software has matured alongside of fractal analysis in neuroscience, and today ImageJ is not a niche but a foundation relied on by a substantial number of neuroscientists for work in diverse fields including fractal analysis. This is largely owing to two features of open-source software leveraged in ImageJ and vital to vigorous neuroscience: customizability and collaboration. With those notions in mind, this chapter's aim is threefold: (1) it introduces ImageJ, (2) it outlines ways this software tool has influenced fractal analysis in neuroscience and shaped the questions researchers devote time to, and (3) it reviews a few examples of ways investigators have developed and used ImageJ for pattern extraction in fractal analysis. Throughout this chapter, the focus is on fostering a collaborative and creative mindset for translating knowledge of the fractal geometry of the brain into clinical reality.

Box-Counting Fractal Analysis: A Primer for the Clinician

This chapter lays out the elementary principles of fractal geometry underpinning much of the rest of this book. It assumes a minimal mathematical background, defines the key principles and terms in context, and outlines the basics of a fractal analysis method known as box counting and how it is used to perform fractal, lacunarity, and multifractal analyses. As a standalone reference, this chapter grounds the reader to be able to understand, evaluate, and apply essential methods to appreciate and heal the exquisitely detailed fractal geometry of the brain.

Retinal microvasculature and vasoreactivity changes in hypertension using optical coherence tomography-angiography

PURPOSE

To evaluate the retinal vasculature and vasoreactivity of patients with hypertension (HTN) using spectral domain optical coherence tomography angiography (SD-OCTA).

METHODS

Patients with and without a diagnosis of HTN were included in this cross-sectional observational study. All eyes were imaged with SD-OCTA using 3 mm × 3 mm and 6 mm × 6 mm centered on both the fovea and optic disk. A second 6 mm × 6 mm scan was taken after a 30 s breath-hold. Vessel density (VD), vessel skeletonized density (VSD), and fractal dimension (FD) were calculated using customized MATLAB scripts. Vessel diameter index (VDI) was obtained by taking the ratio of VD to VSD. Vasoreactivity was measured by subtracting the VD or VSD before and after breath-hold (∆VD, ∆VSD).

RESULTS

Twenty-three eyes with HTN (17 patients) and 17 control eyes (15 patients) were included. In the 6 mm × 6 mm angiogram centered on fovea, the superficial capillary plexus (SCP) VD (ß =  - 0.029, p = 0.012), VSD (ß =  - 0.004, p = 0.043) and the choriocapillaris VD (ß =  - 0.021, p = 0.030) were significantly decreased in HTN compared to control eyes. Similarly, FD was decreased in both the SCP (ß =  - 0.012, p = 0.013) and choriocapillaris (ß =  - 0.009, p = 0.030). In the 3 mm × 3 mm angiogram centered on optic disk, SCP VDI (ß =  - 0.364, p = 0.034) was decreased. ∆VD and ∆VSD were both reduced in the DCP (ß =  - 0.034, p = 0.032; ß =  - 0.013, p = 0.043) and ∆VSD was elevated in the choriocapillaris of HTN eyes (ß = 0.004, p = 0.032).

CONCLUSIONS

The study used SD-OCTA to show significant differences in the retinal vasculature of hypertensive patients. It was also the first to demonstrate the potential of OCT-A to investigate retinal vascular reactivity in patients with HTN.

Optical coherence tomography angiography reveals progressive worsening of retinal vascular geometry in diabetic retinopathy and improved geometry after panretinal photocoagulation

Purpose

To quantify vessel tortuosity and fractal dimension of the superficial capillary plexus (SCP) of the macula in different stages of diabetic retinopathy (DR), and following panretinal photocoagulation (PRP) using optical coherence tomography angiography (OCTA).

Methods

75 eyes of 75 subjects were divided into five groups; healthy controls, diabetes with no clinical DR, non-proliferative diabetic retinopathy (NPDR), proliferative diabetic retinopathy (PDR) and patients who received PRP for PDR (PDR+PRP).For vessel tortuosity, SCP slabs from 3x3 mm macular OCTA scans were processed using imageJ (NIH, USA), where large perifoveal vessels were traced and their length was measured with tortuosity calculated as the ratio between the actual length and the straight Euclidean length. For fractal dimension, SCP slabs were processed and imported to Fractalyse (ThéMA, France), where box-counting analyses produced fractal dimension values.

Results

We found a significant difference in vessel tortuosity and fractal dimension between the five groups (one-way ANOVA, p < 0.001both). NPDR and PDR had significantly more tortuous vessels and lower fractal dimension compared to healthy controls (Tukey HSD: p = 0.02, 0.015,0.015 and <0.001, respectively). Fractal dimension was also significantly lower in NPDR and PDR compared to eyes with no clinical DR (p <0.001 both), and in PDR compared to NPDR (p = 0.014). Following PRP, vessel tortuosity was significantly lower and fractal dimension was higher in PDR+PRP compared to PDR (p = 0.001 and 0.031, respectively).

Conclusions

We used macular OCTA scans to demonstrate significantly higher perifoveal large vessel tortuosity, and lower fractal dimension in NPDR and PDR compared to healthy controls. Vessel tortuosity shows more dramatic normalization than fractal dimension and could be explored as a sensitive marker for successful PRP.

A healthy dose of chaos: Using fractal frameworks for engineering higher-fidelity biomedical systems

Optimal levels of chaos and fractality are distinctly associated with physiological health and function in natural systems. Chaos is a type of nonlinear dynamics that tends to exhibit seemingly random structures, whereas fractality is a measure of the extent of organization underlying such structures. Growing bodies of work are demonstrating both the importance of chaotic dynamics for proper function of natural systems, as well as the suitability of fractal mathematics for characterizing these systems. Here, we review how measures of fractality that quantify the dose of chaos may reflect the state of health across various biological systems, including: brain, skeletal muscle, eyes and vision, lungs, kidneys, tumours, cell regulation, skin and wound repair, bone, vasculature, and the heart. We compare how reports of either too little or too much chaos and fractal complexity can be damaging to normal biological function, and suggest that aiming for the healthy dose of chaos may be an effective strategy for various biomedical applications. We also discuss rising examples of the implementation of fractal theory in designing novel materials, biomedical devices, diagnostics, and clinical therapies. Finally, we explain important mathematical concepts of fractals and chaos, such as fractal dimension, criticality, bifurcation, and iteration, and how they are related to biology. Overall, we promote the effectiveness of fractals in characterizing natural systems, and suggest moving towards using fractal frameworks as a basis for the research and development of better tools for the future of biomedical engineering.

Fractal Dimension in Quantifying Experimental-Pulmonary-Hypertension-Induced Cardiac Dysfunction in Rats

BACKGROUND

Right-sided heart failure has high morbidity and mortality, and may be caused by pulmonary arterial hypertension. Fractal dimension is a differentiated and innovative method used in histological evaluations that allows the characterization of irregular and complex structures and the quantification of structural tissue changes.

OBJECTIVE

To assess the use of fractal dimension in cardiomyocytes of rats with monocrotaline-induced pulmonary arterial hypertension, in addition to providing histological and functional analysis.

METHODS

Male Wistar rats were divided into 2 groups: control (C; n = 8) and monocrotaline-induced pulmonary arterial hypertension (M; n = 8). Five weeks after pulmonary arterial hypertension induction with monocrotaline, echocardiography was performed and the animals were euthanized. The heart was dissected, the ventricles weighed to assess anatomical parameters, and histological slides were prepared and stained with hematoxylin/eosin for fractal dimension analysis, performed using box-counting method. Data normality was tested (Shapiro-Wilk test), and the groups were compared with non-paired Student t test or Mann Whitney test (p < 0.05).

RESULTS

Higher fractal dimension values were observed in group M as compared to group C (1.39 ± 0.05 vs. 1.37 ± 0.04; p < 0.05). Echocardiography showed lower pulmonary artery flow velocity, pulmonary acceleration time and ejection time values in group M, suggesting function worsening in those animals.

CONCLUSION

The changes observed confirm pulmonary-arterial-hypertension-induced cardiac dysfunction, and point to fractal dimension as an effective method to evaluate cardiac morphological changes induced by ventricular dysfunction.

Comparison of fractal dimension and Shannon entropy in myocytes from rats treated with histidine-tryptophan-glutamate and histidine-tryptophan cetoglutarate

INTRODUCTION

Solutions that cause elective cardiac arrest are constantly evolving, but the ideal compound has not yet been found. The authors compare a new cardioplegic solution with histidine-tryptophan-glutamate (Group 2) and other one with histidine-tryptophan-cetoglutarate (Group 1) in a model of isolated rat heart.

OBJECTIVE

To quantify the fractal dimension and Shannon entropy in rat myocytes subjected to cardioplegia solution using histidine-tryptophan with glutamate in an experimental model, considering the caspase markers, IL-8 and KI-67.

METHODS

Twenty male Wistar rats were anesthetized and heparinized. The chest was opened, the heart was withdrawn and 40 ml/kg of cardioplegia (with histidine-tryptophan-cetoglutarate or histidine-tryptophan-glutamate solution) was infused. The hearts were kept for 2 hours at 4ºC in the same solution, and thereafter placed in the Langendorff apparatus for 30 min with Ringer-Locke solution. Analyzes were performed for immunohistochemical caspase, IL-8 and KI-67.

RESULTS

The fractal dimension and Shannon entropy were not different between groups histidine-tryptophan-glutamate and histidine-tryptophan-acetoglutarate.

CONCLUSION

The amount of information measured by Shannon entropy and the distribution thereof (given by fractal dimension) of the slices treated with histidine-tryptophan-cetoglutarate and histidine-tryptophan-glutamate were not different, showing that the histidine-tryptophan-glutamate solution is as good as histidine-tryptophan-acetoglutarate to preserve myocytes in isolated rat heart.

Quantitating the subtleties of microglial morphology with fractal analysis

It is well established that microglial form and function are inextricably linked. In recent years, the traditional view that microglial form ranges between “ramified resting” and “activated amoeboid” has been emphasized through advancing imaging techniques that point to microglial form being highly dynamic even within the currently accepted morphological categories. Moreover, microglia adopt meaningful intermediate forms between categories, with considerable crossover in function and varying morphologies as they cycle, migrate, wave, phagocytose, and extend and retract fine and gross processes. From a quantitative perspective, it is problematic to measure such variability using traditional methods, but one way of quantitating such detail is through fractal analysis. The techniques of fractal analysis have been used for quantitating microglial morphology, to categorize gross differences but also to differentiate subtle differences (e.g., amongst ramified cells). Multifractal analysis in particular is one technique of fractal analysis that may be useful for identifying intermediate forms. Here we review current trends and methods of fractal analysis, focusing on box counting analysis, including lacunarity and multifractal analysis, as applied to microglial morphology.